Problem: Simplify the following expression: $x = \dfrac{n^2 - 12n + 20}{n - 2} $
Solution: First factor the polynomial in the numerator. $ n^2 - 12n + 20 = (n - 2)(n - 10) $ So we can rewrite the expression as: $x = \dfrac{(n - 2)(n - 10)}{n - 2} $ We can divide the numerator and denominator by $(n - 2)$ on condition that $n \neq 2$ Therefore $x = n - 10; n \neq 2$